Seth Godin:

In general, organizations are afraid to fire customers, no matter how unreasonable. This is a mistake. It’s good for you.

Once in a while we (at Marketcircle) have to let a customer go, but it’s usually for the best (for both parties). 

Sometimes telling an unreasonable customer the truth – that it just can’t happen (whatever they’re demanding), is the best solution for your business. Offer a full refund and send them on their way.

If you end things on a positive note they’re more likely to return someday and keep the word of mouth to a minimum.